## Osaka Journal of Mathematics

### On the splitting principle of bundle gerbe modules

Atsushi Tomoda

#### Abstract

We introduce the notion of an $n$-trivialization and a compatible curving and construct the splitting of bundle gerbe modules to define the twisted Chern classes and the twisted Chern character for bundle gerbe modules in terms of algebraic topology. Moreover, we prove that the latter coincides with the twisted Chern character due to Bouwknegt-Carey-Mathai-Murray-Stevenson [1] if the bundle gerbe is given an $n$-trivialization and a compatible curving.

#### Article information

Source
Osaka J. Math. Volume 44, Number 1 (2007), 231-246.

Dates
First available in Project Euclid: 19 March 2007

https://projecteuclid.org/euclid.ojm/1174324334

Mathematical Reviews number (MathSciNet)
MR2313038

Zentralblatt MATH identifier
1133.19002

#### Citation

Tomoda, Atsushi. On the splitting principle of bundle gerbe modules. Osaka J. Math. 44 (2007), no. 1, 231--246.https://projecteuclid.org/euclid.ojm/1174324334

#### References

• P. Bouwknegt, A. Carey, V. Mathai, M.K. Murray, and D. Stevenson: Twisted $K$-theory and $K$-theory of bundle gerbes, Comm. Math. Phys. 228 (2002), 17--45.
• M.K. Murray: Bundle gerbes, J. London. Math. Soc. (2) 54 (1996), 403--416.
• M.K. Murray and D. Stevenson: Bundle gerbes: stable isomorphism and local theory, J. London. Math. Soc. (2) 62 (2000), 925--937.
• D. Husemoller: Fibre Bundles, second edition, Graduate Texts in Math. 20, Springer-Verlag, New York, 1975.